Friday, January 8, 2016

Favorite comments of '15, cont: Anonymouses and SteveH

On Math problems of the week: from the "reform math" curriculum at Phillips Exeter Academy:

Anonymous said...
I looked at the Exeter problems a few years ago and I like them. I would hesitate to call them "reform," though. If I remember correctly, quite a few of the problems require substantial knowledge of Algebra to solve them.

I think that this approach is basically a "sink or swim" situation. As a teacher in the public sphere, I think about what I would have to teach so that students would be capable of solving, or even engaging in a solution of these problems. The Exeter situation seems to assume that their students come to them WITH the skills, which are then honed through solving these problems. Either that or those who can't solve them fail out - at Exeter that the way it goes. But at public schools, we don't have that luxury, we need to teach these skills rather than only identify the students who either already know them, or acquire them independently. Now, this is not to say that the teachers at Exeter aren't teaching, but I believe that it is a very different environment than what we face in the public sphere.

It reminds me of the Juku system in Japan where the skills and practice are handled by the private cram schools while the public schools simply assume that everybody (who is anybody) will be paying for the Juku and thus the public schools focus almost exclusively on conceptual problem solving.

The Japanese style problems are here:

Again, I would hesitate to call these reform problems because they require so much real mathematical knowledge.

An interesting comment of the juku phenomenon is here:


SteveH said...
Andover (more traditional) and Exeter (Harkness Table) are two opposing pedagogies that seem to work well in their own ways, but Exeter's use of oval table discussions bears little resemblance to anything the usual "reform" K-12 math pedagogues push. Exeter's students also have enormous homework requirements and have to come prepared to take a position and defend it. It's not a hands-on, engagement-driven, "trust the spiral" approach. However, I'm still not a fan of the Harkness Table because it's too easy to get wrong and waste time. Then again, a poorly prepared teacher can waste a lot of time. However, Andover and Exeter are populated with driven (internally or externally), high achieving students. Both schools go out of their ways to bring in top math students. I was considering each for my son and Andover would be the choice, but I decided to save a LOT of money and stick with our AP-pushing public high school. This is JUST high school material and both schools don't have some magic "understanding" formula outside of pushing and hard work, and they don't try to go further than AP Calculus. They just push the AMC math contests. Actually, I'm rather annoyed that AMC is now the "beyond" score of choice for colleges.

Anonymous said...
If the case of the son of a family connection is typical, Exeter expects incoming freshman - at least those not coming from known prep schools or very high-performing publics- to have completed their freshman year at their previous schools. This was also true at an another big-name New England school, when another family connection entered. Both kids had been good students - I don't know details - at academically solid public high schools. As the old non-PC, saying goes; if you want better schools, get better students.

Anonymous said...
I could do these, but I'd have to privilege the symbol. Is that allowed?

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